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Ideal Weyl semimetals, similar to graphene, show peculiar features such as exotic electronic transport. Here, Ruan et al. predict that strain-tuned HgTe-class materials can become ideal Weyl semimetals, which could provide a promising platform to study emergent topological phenomena.

A flat stanene layer can be grown on Cu (111) by MBE growth, exhibiting topological properties as revealed by a combination of ARPES, STM and DFT calculations.

Quantum spin Hall edge states are protected by time-reversal symmetry and are expected to disappear in a strong magnetic field. Here, the authors use microwave impedance microscopy and find, surprisingly, edge conduction in mercury telluride quantum wells that survives up to 9 T with little change.

First-principles calculations predict that Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ are topological insulators—three-dimensional semiconductors with unusual surface states generated by spin–orbit coupling—whose surface states are described by a single gapless Dirac cone. The calculations further predict that Bi₂Se₃ has a non-trivial energy gap larger than the energy scale k_BT at room temperature.

Axions are hypothetical particles that might play an important part in particle physics, astrophysics and cosmology. So far they have eluded observation, but theoretical work now predicts that axion physics might be explored in condensed-matter systems known as topological insulators.

The growth of stanene on bismuth telluride has been achieved using molecular beam epitaxy. Photoemission spectroscopy and theoretical calculations are used to investigate the effects of the substrate on the electronic properties of the Sn layers.

The quantum spin Hall state is predicted to consist of two oppositely polarized spin currents travelling in opposite directions around the edges of a topological insulator. Non-local measurements of the transport in HgTe quantum wells confirm the polarized nature of these edge states.

The gapless surface states of topological insulators could enable quantitatively different types of electronic device. A study of the topological insulating Bi₂Se₃ thin films finds that a gap in these states opens up in films below a certain thickness. This in turn suggests that in thicker films, gapless states exist on both upper and lower surfaces.

The electric field generated by a gate electrode is exploited to trigger a reversible ferromagnetic–paramagnetic phase transition in a magnetic topological insulator close to a quantum critical point.

Stanene is a single sheet of tin atoms. Here, it is shown that a few stacked layers of stanene can be a superconductor. Changing the thickness of the substrate modifies the form of superconductivity and critical temperature.

An almost ideal quantum anomalous Hall state is observed in (Bi,Sb)Te films doped with vanadium. This state is reached without the application of a polarizing magnetic film, making these materials interesting for low-power electronic applications.

Intercalation of copper and cobalt atoms into n-type SnS₂ enables seamless integration of metal, and n- and p-type semiconductors in one parent 2D material.

The axis of a spinning electron tends to remain fixed in direction: in contrast, an electron moving in a semiconductor sees a lattice of charged atoms flying past, causing its spin direction to fluctuate. Koralek and colleagues demonstrate that an electric field applied to the semiconductor can balance this spin-destabilizing effect; the collective spin of the entire gas of electrons is conserved, a property well-suited for 'spintronics' applications.

The prediction of an antiferromagnetic semimetal that breaks both time-reversal and inversion symmetry but respects their combination could provide a platform for studying the interplay between Dirac fermions and magnetism.

The existence of topological conducting surfaces on insulators has been demonstrated by angular photoemission spectroscopy, but the number of transport experiments on these systems have so far been scarce. Transport evidence of topological surface states is now shown in Bi₂Se₃ nanoribbons through the observation of Aharonov–Bohm oscillations.

Topological insulators have been predicted and recently demonstrated experimentally in a series of binary alloys. It is now show theoretically that about 50 Heusler compounds show features similar to those of the confirmed topological insulator HgTe, which considerably expands the possibility of realizing quantum topological phenomena.

Quantum spin Hall insulators are new states of matter that were recently predicted and observed. A theoretical work now explores distinct experimental manifestations resulting from the exotic behaviour that characterizes these structures.

Electrochemical ion intercalation in 2D layered materials is known to occur through the material’s edges, accompanied by frequent structural deformations. Here the authors show that in MoS2 flakes where the edges have been sealed, a reversible and ion-selective intercalation occurs through the top surface via the intrinsic defects.

A spin- and valley-polarized photocurrent is generated, in an electric double-layer transistor, with a direction and magnitude that depends on the degree of circular polarization of the incident radiation and on an external electric field.

The quantum anomalous Hall effect is a recently demonstrated chiral transport phenomenon arising in magnetically doped topological insulators. Here, the authors study the Hall plateau switching and universal phase diagram of the quantum anomalous Hall effect in thin films of two-dimensional Cr-doped (BiSb)₂Te₃.

The anisotropic optical properties of black phosphorus can be exploited to fabricate photodetectors with linear dichroism operating over a broad spectral range.

The current state-of-the-art and possible future developments on two-dimensional silicene, germanene, and stanene sheets (called 2D-Xenes), and their ligand-functionalized derivatives (Xanes), are discussed.

This Perspective discusses recent progress in the field of topological states in condensed matter; initiated by the quantum Hall effect, it now includes systems like topological insulators, topological superconductors, and Weyl/Dirac semimetals.